You can adjust the tension on the bobbin wider by turning the screw you see in the front of it (on the bed of the machine). I've not had your specific problem, but often get the bobbin winding mechanism going too fast and the thread will jump off the spool pin and the thread wraps around the post where you put the bobbin.
The first thing I would do is play with adjusting the tension (both tightening and loosening) to see if you can make it work right. My guess it's either too tight and the thread won't seat between the discs or it's too loose and the thread pops out. If that doesn't work I'd work with the speed you are using to wind the thread with slowing and speeding up with your foot controller so see if there is a speed where it works correctly (I'm suggesting that because of my experience).
Something to think about is that thread spools aren't as heavy as they were when this machine is made. When this machine was made, all the spools were wooden. So, if you still don't have a satisfactory solution is to put some kind of weight on the top of the thread spool to make it heavier (coin, washer, fishing weight) and see if that helps.
bkay